Question

If one root of the quadratic equation $x^2 + 3x - p = 0$ is 2, then find the value of $p$.

Hint:

When one root is known, substitute it into the quadratic equation to find the missing constant.

Answer 1

Step 1: Substitute $x = 2$ in the equation.
\[ (2)^2 + 3(2) - p = 0 \Rightarrow 4 + 6 - p = 0 \]
Step 2: Simplify to find $p$.
\[ 10 - p = 0 \Rightarrow p = 10 \]
Step 3: Conclusion.
Therefore, the value of $p$ is 10.